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Two regularization methods for a Cauchy problem for the Laplace equation. (English) Zbl 1132.35493
Summary: A Cauchy problem for the Laplace equation in a rectangle is considered. Cauchy data are given for $y=0$, and boundary data are prescribed for $x=0$ and $x=\pi $. The solution is sought for $0<y\leqslant 1$. We propose two different regularization methods for the ill-posed problem based on separation of variables. Both methods are applied to find regularized solutions which are stably convergent to the exact one with explicit error estimates.

MSC:
35R25Improperly posed problems for PDE
35J25Second order elliptic equations, boundary value problems
35B35Stability of solutions of PDE
35A35Theoretical approximation to solutions of PDE
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References:
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